Question

if x^2+y^2=3xy then prove that 2log(x-y) =logx+logy

Answer 1

$= > {x}^{2} + {y}^{2} - 2xy = xy \\ = > {(x - y)}^{2} = xy \\ now \: take \: log \: both \: the \: sides \\ = > log( {(x - y)}^{2} ) = log(xy) \\ = > 2 log(x - y) = log(x) + log(y)$
properties used here are

$log( {a}^{b} ) = b \: \: log(a) \\ log(ab) = log(a) + log(b)$

for this question to be valid x and y should be positive real number.